Sliding mode and active disturbance rejection control to stabilization of one-dimensional anti-stable wave equations subject to disturbance in boundary input

Guo, Bao‐Zhu; Jin, Feng‐Fei; Yao, Cui-Zhen

doi:10.1109/cdc.2012.6427033

Cited by 52 publications

(99 citation statements)

References 11 publications

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“…In most of literatures about ADRC in PDE systems, the disturbance estimation converges asymptotically to the true value of the disturbance [7], [9]. The state feedback designs, using ADRC, of an one-dimensional anti-stable wave equation and a generalized version of the wave equation subject to matched disturbances d(t) were presented in [6], [12]. The output feedback design of an one-dimensional antistable wave equation with a boundary disturbance d(t) was developed in [7].…”

Section: Introductionmentioning

confidence: 99%

Disturbance Estimation of a Wave PDE on a Time-varying Domain

Wang¹,

Pi²,

Krstić³

2017

2017 Proceedings of the Conference on Control and Its Applications

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In this paper, we design an exponentially convergent disturbance observer for a wave PDE on a time-varying domain by using two boundary measurements u(0, t), ut(l(t), t). More specifically, two auxiliary PDEs are constructed to build the disturbance observer for tracking the external disturbance in the wave PDE. Exponential convergence of the disturbance estimation to the true disturbance value is proved by Lyapunov analysis, and all states in the observer are shown to be bounded once the original state u(x, t) is bounded via designing control input.

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Section: Introductionmentioning

confidence: 99%

Disturbance Estimation of a Wave PDE on a Time-varying Domain

Wang¹,

Pi²,

Krstić³

2017

2017 Proceedings of the Conference on Control and Its Applications

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“…Because the state locus can be designed, and not related to the system parameters and outside disturbance, it has a strong robustness [18]. Sliding mode variable structure control has three basic problems: firstly, the sliding mode should exist; secondly, the reach-ability condition should be satisfied; finally, the stability of the sliding mode should be analyzed [19][20][21]. The mathematical model of the BIM in the two-phase stationary -coordinate system and with the torque winding stator current and stator flux as state variables is as follows:…”

Section: Sliding Mode Variable Structure Directmentioning

confidence: 99%

A Bearingless Induction Motor Direct Torque Control and Suspension Force Control Based on Sliding Mode Variable Structure

Yang

Chen

Sun

et al. 2017

Mathematical Problems in Engineering

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Aiming at the problems of the large torque ripple and unstable suspension performance in traditional direct torque control (DTC) for a bearingless induction motor (BIM), a new method of DTC is proposed based on sliding mode variable structure (SMVS). The sliding mode switching surface of the torque and flux linkage controller are constructed by torque error and flux error, and the exponential reaching law is used to design the SMVS direct torque controller. On the basis of the radial suspension force mathematical model of the BIM, a radial suspension force closed-loop control method is proposed by utilizing the inverse system theory and SMVS. The simulation models of traditional DTC and the new DTC method based on SMVS of the BIM are set up in the MATLAB/Simulink toolbox. On this basis, the experiments are carried out. Simulation and experiment results showed that the stable suspension operation of the BIM can be achieved with small torque ripple and flux ripple. Besides, the dynamic response and suspension performance of the motor are improved by the proposed method.

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“…This control technology does not need accurate model information and it either does not need to assume that the model is linear or bound, therefore it can deal with a large range of uncertain systems [8][9][10]. In fact, the strong robust property of ADRC owes to the introduction of Extended State Observer (ESO), which can estimate the current uncertain dynamics of system more accurately and then make compensations to the control system.…”

Section: Introductionmentioning

confidence: 99%

Compound Controller for DC Motor Servo System Based on Inner-Loop Extended State Observer

Yang

2016

Cybernetics and Information Technologies

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Sliding mode and active disturbance rejection control to stabilization of one-dimensional anti-stable wave equations subject to disturbance in boundary input

Cited by 52 publications

References 11 publications

Disturbance Estimation of a Wave PDE on a Time-varying Domain

Disturbance Estimation of a Wave PDE on a Time-varying Domain

A Bearingless Induction Motor Direct Torque Control and Suspension Force Control Based on Sliding Mode Variable Structure

Compound Controller for DC Motor Servo System Based on Inner-Loop Extended State Observer

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